Use the option quote information shown here to answer the questions that follow.
ID: 2795909 • Letter: U
Question
Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $29.
Suppose you buy 12 contracts of the February 31 call option. How much will you pay, ignoring commissions?
Suppose you buy 12 contracts of the February 31 call option. Macrosoft stock is selling for $32 per share on the expiration date.
On the expiration date, Macrosoft is selling for $25 per share. How much is your options investment worth?
What is your net gain or loss if Macrosoft is selling for $27 at expiration? (Enter your answer as a positive value.)
What is your net gain or loss if Macrosoft is selling For $33 at expiration? (Enter your answer as a positive value.)
What is the break-even stock price? (Round your answer to 2 decimal places, (e.g., 32.16).)
Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $29.
Explanation / Answer
(a) Option Premium on Feb 31 contracts = 0.43 $. Therefore, cost of 12 contracts = 12 x 0.43 = 5.16 $
(b1) Strike Price of Macrosoft Stock (on Feb 31 contracts) = $31 and Underlying Stock Price at expiry =$ 32
Therefore, payoff per option = Underlying Stock price at expiry less Strike Price = 32 - 31 =$1 per contract
Therefore, for 12 contracts total payoff of the investment = 12 x 1 =$12
Net Gain on Investment = Total payoff on investment Less Cost of purchasing 12 options (from part (a))
= 12 -5.16 = $ 6.84
(b2) If Terminal stock price is $31 which is same as the stock price then the investor does not make any loss or gain from buying 12 call options. The investors only loss is the initial cost incurred in purchasing the 12 contracts for $5.16.
Therefore, net payoff = $ 0
(c1) Premium on August 31 put options =$2.3
Therefore, cost of purchasing 12 Aug 31 put options = 2.3 x 12 = $ 27.6
The investor will make maximum gain when the underlying stock price becomes zero and yet the investor is able to sell those zero value stocks at 31$ (the put strike price) a piece owing to holding the put option.
Therefore, payoff from each contract in maximum gain condition = $31 and Total Payoff = 31x12 =$372
Therefore, resultant maxmimum gain = Total payoffs from put options Less Cost of Purchasing 12 puts = 372 - 27.6 = $344.4
(c2) Strike Price of Put =31$ and Stock Price =$25. Therefore, profit on every put option = 31-25=$6
Therefore, position value = 12 x 6 = 72$
(c3) Profit from Put Option Position = $72 and Cost of Purchasing Put Options = $ 27.6
Therefore, Net Gain = Profit from Option position Less Cost of Purchasing Puts = 72 - 27.6 = $ 44.4
(d1) Premium on one Aug 31 put =$2.3
Cash Inflow on selling 12 Aug 31 put options = 12 x 2.3 = $27.6
Strike Price = 31$ and Market Value = $27. Therefore, Loss in Put Option Position = 12 x (31 - 27) = $48
Therefore, Net Loss = Loss from Put Position Less Cash Inflow from Selling Put = 48 - 27.6 = $ 20.4
(d2) Strike Price =$31 and Market Price =$33
Gain in Option Position = 12 x (33-31) = $24 and Cash Inflow from Sale of Put=$27.6
Therefore, Net Gain = Gain in Option Position + Cash Inflow from Sale of Put = 24 + 27.6 =$ 51.6
(d3) Break Even Stock Price would be one which would be equalize the loss in option position to the gain in cash flow from selling options
Now let this price be K . Then net loss on option position with strike price =$31 will be (31 - K) x 12.
For break even, Net Loss in Option Position = Cash Gained from selling Put
( 31 - K ) x 12 = 27.6 Solving thsi equation gives K= $28.7
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